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a: \(\left(-\dfrac{3}{7}\right)^2=\dfrac{\left(-3\right)^2}{7^2}=\dfrac{9}{49}\)
b: \(\dfrac{5}{17}+\dfrac{-15}{34}\cdot\dfrac{2}{5}\)
\(=\dfrac{5}{17}-\dfrac{15}{5}\cdot\dfrac{2}{34}\)
\(=\dfrac{5}{17}-\dfrac{1}{17}\cdot3=\dfrac{2}{17}\)
c: \(\dfrac{-7}{21}+\left(1+\dfrac{1}{3}\right)\)
\(=-\dfrac{1}{3}+1+\dfrac{1}{3}\)
=1
d: \(\left(-\dfrac{1}{5}+\dfrac{3}{12}\right)+\dfrac{-3}{4}\)
\(=\dfrac{-1}{5}+\dfrac{1}{4}-\dfrac{3}{4}\)
\(=\dfrac{-1}{5}-\dfrac{2}{4}\)
\(=\dfrac{-1}{5}-\dfrac{1}{2}=\dfrac{-7}{10}\)
a, 5/-14. 7/-19=8/38
b, -15/4 .( 16/-25 )=12/5
c, 3/-10 .( -15/-2 )=
d, -5/7 . ( 21/-10 )=-9/4
e, 10/-3. (6/-5)==4
f, 21/-9 . ( -6/14 )=1
g, -10/9 . ( 36/20 )=-2
2:
a: \(2^2\cdot3-4=4\cdot3-4=12-4=8\)
b: \(16-2^3\cdot2=16-2^4=16-16=0\)
c: \(4^2-4\cdot2=16-8=8\)
d: \(3^3-2\cdot3^2=27-2\cdot9=27-18=9\)
e: \(7^2-9\cdot2^2=49-9\cdot4=49-36=13\)
f: \(2^2\cdot3+4^2=4\cdot3+16=12+16=28\)
Bài 1:
a: \(13+21\cdot5-\left(198:11-8\right)\)
\(=13+105-18+8\)
=21+87
=108
b: \(272:16-5+4\cdot\left(30-5-255:17\right)\)
\(=17-5+4\cdot\left(30-5-15\right)\)
\(=12+4\cdot10=12+40=52\)
c: \(15\cdot24-14\cdot5\cdot\left(145:5-27\right)\)
\(=360-70\left(29-27\right)\)
=360-140
=220
d: \(18\cdot3-18\cdot2+3\cdot\left(\dfrac{51}{17}\right)\)
\(=18\left(3-2\right)+3\cdot3\)
=18+9
=27
e: \(64+115+36-25\cdot8\cdot6\cdot2^2\cdot3+4^2\)
\(=100+115-200\cdot6\cdot4\cdot3+16\)
\(=231-14400=-14169\)
f: \(15\cdot8-\left(17-30+83\right)-144:6\)
\(=120-24-\left(100-30\right)\)
=96-70
=26
Bài 1:
a) \(\frac{16}{15}.\frac{\left(-5\right)}{14}.\frac{54}{24}.\frac{56}{21}\)
\(=\frac{4.2.2}{5.3}.\frac{\left(-5\right)}{2.7}.\frac{3.3}{4}.\frac{8}{3}\)
\(=\frac{4.2.2.\left(-5\right).3.3.8}{5.3.2.7.4.3}\)
\(=\frac{-16}{7}\)
b) \(\frac{7}{3}.\frac{\left(-5\right)}{2}.\frac{15}{21}.\frac{4}{\left(-5\right)}\)
\(=\frac{7}{3}.\frac{\left(-5\right)}{2}.\frac{5}{7}.\frac{2.2}{\left(-5\right)}\)
\(=\frac{7.\left(-5\right).5.2.2}{3.2.7.\left(-5\right)}\)
\(=\frac{10}{3}\)
Bài 2:
a) \(\frac{21}{24}.\frac{11}{9}.\frac{5}{7}=\frac{7}{8}.\frac{11}{9}.\frac{5}{7}=\frac{11.5}{8.9}=\frac{55}{72}\)
b) \(\frac{5}{23}.\frac{17}{26}+\frac{5}{23}.\frac{9}{26}\)
\(=\frac{5}{23}.\left(\frac{17}{26}+\frac{9}{26}\right)=\frac{5}{23}.1=\frac{5}{23}\)
c) \(\left(\frac{3}{29}-\frac{1}{5}\right).\frac{29}{3}=\frac{3}{29}.\frac{29}{3}-\frac{1}{5}.\frac{29}{3}\)
\(=1-1\frac{14}{15}=\frac{14}{15}\)
Bài 3:
a) x/5 = 2/5
=> x =2
b) -4/x = 20/14 = 10/7
=> -4/x = 10/7
=> x.10 = (-4).7
x.10 = - 28
x= -28 :10
x= -2,8
c) 4/7 = 12/x = 12/ 21
=> 12/x = 12/21
=> x = 21
d) 3/7 = x / 21 = 9/21
=> x/21 = 9/21
=> x= 9
a) Ta có: \(\frac{16}{15}\cdot\frac{-5}{14}\cdot\frac{54}{24}\cdot\frac{56}{21}\)
\(=\frac{16}{15}\cdot\frac{-5}{14}\cdot\frac{9}{4}\cdot\frac{8}{3}\)
\(=4\cdot\frac{-1}{3}\cdot\frac{4}{7}\cdot3\)
\(=12\cdot\frac{-4}{21}=\frac{-48}{21}=\frac{-16}{7}\)
b) Ta có: \(5\cdot\frac{7}{5}=\frac{35}{5}=7\)
c) Ta có: \(\frac{1}{7}\cdot\frac{5}{9}+\frac{5}{9}\cdot\frac{1}{7}+\frac{5}{9}\cdot\frac{3}{7}\)
\(=\frac{5}{9}\left(\frac{1}{7}+\frac{1}{7}+\frac{3}{7}\right)\)
\(=\frac{5}{9}\cdot\frac{5}{7}=\frac{25}{63}\)
d) Ta có: \(4\cdot11\cdot\frac{3}{4}\cdot\frac{9}{121}\)
\(=\frac{4\cdot11\cdot3\cdot9}{4\cdot121}=\frac{27}{11}\)
e) Ta có: \(\frac{3}{4}\cdot\frac{16}{9}-\frac{7}{5}:\frac{-21}{20}\)
\(=\frac{4}{3}+\frac{4}{3}=\frac{8}{3}\)
g) Ta có: \(2\frac{1}{3}-\frac{1}{3}\cdot\left[\frac{-3}{2}+\left(\frac{2}{3}+0,4\cdot5\right)\right]\)
\(=\frac{7}{3}-\frac{1}{3}\cdot\left[\frac{-3}{2}+\frac{2}{3}+2\right]\)
\(=\frac{7}{3}-\frac{1}{3}\cdot\frac{7}{6}\)
\(=\frac{7}{3}-\frac{7}{18}=\frac{42}{18}-\frac{7}{18}=\frac{35}{18}\)
`@` `\text {Ans}`
`\downarrow`
`1,`
`a)`
`-7/25 + (-8)/25`
`= (-7 - 8)/25`
`= -15/25`
`= -3/5`
`b)`
`6/13 + (-15)/39`
`= 18/39 + (-15)/39`
`= (18 - 15)/39`
`= 3/39`
`= 1/13`
`c)`
`5/7 + 4/(-14)`
`= 10/14 + (-4)/14`
`= (10 - 4)/14`
`= 6/14`
`= 3/7`
`d)`
`-8/18 + (-15)/27`
`= -4/9 + (-5)/9`
`= (-4-5)/9`
`= -9/9 = -1`
`2,`
`a)`
`3/5 + (-7)/4`
`= 12/20 + (-35)/20`
`= (12 - 35)/20`
`=-23/20`
`b)`
`(-2) + (-5)/8`
`= (-16)/8 + (-5)/8`
`= (-16 - 5)/8`
`= -21/8`
`c)`
`1/8 + (-5)/9`
`= 9/72 + (-40)/72`
`= (9-40)/72`
`= -31/72`
`d)`
`6/13 + (-14)/39`
`= 18/39 + (-14)/39`
`= (18 - 14)/39`
`= 4/39`
`e)`
`(-18)/24 + 15/21`
`= (-3)/4 + 5/7`
`= (-21)/28 + 20/28`
`= (-21 + 20)/28`
`= -1/28`
\(\left(\dfrac{5}{7}-\dfrac{7}{7}\right)-\left[0,2-\left(-\dfrac{2}{7}-\dfrac{1}{10}\right)\right]\)
=\(-\dfrac{2}{7}-\left[\dfrac{1}{5}+\dfrac{2}{7}+\dfrac{1}{10}\right]\)
=\(-\dfrac{2}{7}-\dfrac{1}{5}-\dfrac{2}{7}-\dfrac{1}{10}\)
=\(\left(-\dfrac{2}{7}-\dfrac{2}{7}\right)-\left(\dfrac{1}{5}+\dfrac{1}{10}\right)\)
=\(-\dfrac{4}{7}-\left(\dfrac{2}{10}+\dfrac{1}{10}\right)\)
=\(-\dfrac{4}{7}-\dfrac{3}{10}\)
=\(-\dfrac{40}{70}-\dfrac{21}{70}\)
=\(-\dfrac{61}{70}\)
(3 - \(\dfrac{1}{4}\) + \(\dfrac{2}{3}\)) - (5 - \(\dfrac{1}{3}\) - \(\dfrac{5}{6}\)) - (6 - \(\dfrac{7}{4}\) - \(\dfrac{3}{2}\))
= 3 - \(\dfrac{1}{4}\) + \(\dfrac{2}{3}\) - 5 + \(\dfrac{1}{3}\) + \(\dfrac{5}{6}\) - 6 + \(\dfrac{7}{4}\) + \(\dfrac{3}{2}\)
= (3 - 5 - 6) + ( \(\dfrac{7}{4}\) - \(\dfrac{1}{4}\)) + (\(\dfrac{2}{3}\) + \(\dfrac{1}{3}\)) + \(\dfrac{3}{2}\) + \(\dfrac{5}{6}\)
= - 8 + \(\dfrac{3}{2}\) + 1 + \(\dfrac{3}{2}\) + \(\dfrac{5}{6}\)
= (- 8 + 1) + (\(\dfrac{3}{2}\) + \(\dfrac{3}{2}\)) + \(\dfrac{5}{6}\)
= -7 + 3 + \(\dfrac{5}{6}\)
= - 4 + \(\dfrac{5}{6}\)
= \(\dfrac{-19}{6}\)
a: \(\dfrac{16}{15}\cdot\dfrac{-5}{14}\cdot\dfrac{54}{24}\cdot\dfrac{56}{21}\)
\(=\dfrac{16}{24}\cdot\dfrac{-5}{15}\cdot\dfrac{54}{21}\cdot\dfrac{56}{14}\)
\(=\dfrac{2}{3}\cdot\dfrac{-1}{3}\cdot\dfrac{18}{7}\cdot4\)
\(=\dfrac{-2\cdot2\cdot4}{7}=-\dfrac{16}{7}\)
b: \(\dfrac{7}{3}\cdot\dfrac{-5}{2}\cdot\dfrac{15}{21}\cdot\dfrac{4}{-5}\)
\(=\dfrac{7}{3}\cdot\dfrac{5}{7}\cdot\dfrac{5}{2}\cdot\dfrac{4}{5}\)
\(=\dfrac{5}{3}\cdot\dfrac{4}{2}=\dfrac{5}{3}\cdot2=\dfrac{10}{3}\)
c: \(\left(-\dfrac{2}{5}+\dfrac{1}{3}\right)\left(\dfrac{3}{2}-\dfrac{3}{7}\right)\)
\(=\dfrac{-2\cdot5+3}{15}\cdot\dfrac{3\cdot7-3\cdot2}{14}\)
\(=\dfrac{-7}{15}\cdot\dfrac{15}{14}=\dfrac{-7}{14}=-\dfrac{1}{2}\)
d: \(\left(\dfrac{1}{2}-\dfrac{1}{3}\right)\left(5-\dfrac{1}{4}\right)\)
\(=\dfrac{3-2}{6}\cdot\dfrac{20-1}{4}\)
\(=\dfrac{1}{6}\cdot\dfrac{19}{4}=\dfrac{19}{24}\)
e: \(\left(\dfrac{4}{5}\right)^2=\dfrac{4^2}{5^2}=\dfrac{16}{25}\)